Victoria is on a class field trip. While riding over a bridge, she notices that the road and the structure of the bridge make a variety of lines. She believes that the posts of the bridge are perpendicular to the road. What can she say to prove this to her classmates?

In this concept, you will learn how to identify parallel, intersecting and perpendicular lines.

Identifying Parallel and Perpendicular Lines

Lines exist in space. Two lines intersect when they cross each other. Because all lines are straight, intersecting lines can only cross each other once. Look at the examples below. Imagine the lines extend beyond the picture, on forever.

Two lines that form right angles when they intersect are perpendicular lines. All four angles formed by the perpendicular lines measure \begin{align*}90^\circ\end{align*}. If any of the four angles is marked with the small box, the lines are perpendicular. Take a look at the perpendicular lines below.

Lines that never intersect are parallel lines. Parallel lines do not form any angles. Parallel lines look like railroad tracks: they are always the same distance apart, running next to each other.

Identify whether the pairs of lines are parallel, perpendicular, or intersecting.

First, look to see if the lines intersect.

The lines do not intersect.

Next, determine if the lines would intersect if they were extended.

No

Then, label the lines as parallel, perpendicular or intersecting.

The lines are parallel.

The answer is that the lines are parallel.

First, look to see if the lines intersect.

The lines do intersect.

Next, determine if the lines intersect at a right angle.

The lines do not intersect at a right angle.

Then, label the lines as parallel, perpendicular or neither.

The lines are intersecting.

The answer is that the lines are intersecting but not perpendicular.

Examples

Example 1

Earlier, you were given a problem about Victoria and the bridge.

As she rides across the bridge, she notices the different lines. What can she say to prove that the posts are perpendicular to the road?

First, treat the posts and the road like lines. Look to see if the lines intersect.

They do intersect.

Next, determine if the lines intersect the road at a right angle.

The lines do intersect at a right angle.

Then, label the lines as parallel, perpendicular or neither.

The lines are perpendicular.

The answer is that the lines are perpendicular.

Example 2

Identify whether the pair of lines are parallel, perpendicular or intersecting.